A153263 a(n) = A014217(n+3) - A014217(n).

3, 5, 9, 13, 23, 35, 59, 93, 153, 245, 399, 643, 1043, 1685, 2729, 4413, 7143, 11555, 18699, 30253, 48953, 79205, 128159, 207363, 335523, 542885, 878409, 1421293, 2299703, 3720995, 6020699, 9741693, 15762393, 25504085, 41266479, 66770563

Offset

0,1

Comments

The least significant digits are a sequence of period length 4: 3,5,9,3.

One could extend A014217 using its recurrence to define A014217(-1)=-1. This would add a(-1)=3 here by definition, and the least significant digits would still follow the (same, wrapped) period of length 4: 3,3,5,9.

Links

Table of n, a(n) for n=0..35.

Index entries for linear recurrences with constant coefficients, signature (0,2,1).

Formula

a(2n+2) = a(2n+1) + a(2n) + 1. a(2n+3) = a(2n+2) + a(2n+1) - 1.

From R. J. Mathar, Feb 07 2009, Apr 18 2009: (Start)

a(n) = 2*a(n-2) + a(n-3) = (-1)^n + 2*A000032(n+1).

G.f.: (3+5x+3x^2)/ ((1+x)(1-x-x^2)). (End)

a(n) + a(n+1) = A022112(n+2). - R. J. Mathar, Feb 25 2013

a(n) = ((-2)^n + (1 - sqrt(5))^(1+n) + (1 + sqrt(5))^(1+n))/2^n. - Stefano Spezia, Dec 25 2021

Mathematica

LinearRecurrence[{0, 2, 1}, {3, 5, 9}, 40] (* Harvey P. Dale, Jun 23 2022 *)

Crossrefs

Cf. A022112.

Sequence in context: A052282 A001993 A284829 * A295140 A144933 A133033

Adjacent sequences: A153260 A153261 A153262 * A153264 A153265 A153266

Keyword

nonn,easy

Author

Paul Curtz, Dec 22 2008

Extensions

More terms from R. J. Mathar, Feb 07 2009

Edited by R. J. Mathar, Apr 18 2009

Status

approved